diff --git a/libs/papers/Data/Description/Indexed.idr b/libs/papers/Data/Description/Indexed.idr
index 5030dd2e0..b4b266163 100644
--- a/libs/papers/Data/Description/Indexed.idr
+++ b/libs/papers/Data/Description/Indexed.idr
@@ -5,7 +5,7 @@
 
 module Data.Description.Indexed
 
-%default covering
+%default total
 
 public export
 data IDesc : (p : Type -> Type) -> (i : Type) -> Type where
@@ -16,7 +16,7 @@ data IDesc : (p : Type -> Type) -> (i : Type) -> Type where
   (+) : (d1, d2 : IDesc p i) -> IDesc p i
   Sig : (s : Type) -> p s -> (s -> IDesc p i) -> IDesc p i
 
-total public export
+public export
 Elem : IDesc p i -> (i -> Type) -> Type
 Elem Zero x = Void
 Elem One x = ()
@@ -27,7 +27,7 @@ Elem (Sig s prop d) x = (v : s ** Elem (d v) x)
 
 public export
 data Fix : (i -> IDesc p i) -> i -> Type where
-  MkFix : Elem (d i) (Fix d) -> Fix d i
+  MkFix : assert_total (Elem (d i) (Fix d)) -> Fix d i
 
 namespace Example
 
@@ -35,7 +35,7 @@ namespace Example
   VecD a 0 = One
   VecD a (S n) = Sig a () (const (Id n))
 
-export total
+export
 map : (d : IDesc p i) -> ((v : i) -> x v -> y v) -> Elem d x -> Elem d y
 map Zero f v = v
 map One f v = v
@@ -45,8 +45,8 @@ map (d1 + d2) f (Left v) = Left (map d1 f v)
 map (d1 + d2) f (Right v) = Right (map d2 f v)
 map (Sig s _ d) f (x ** v) = (x ** map (d x) f v)
 
-export covering
+export
 ifold : {d : i -> IDesc p i} ->
         ((v : i) -> Elem (d v) x -> x v) ->
         {v : i} -> Fix d v -> x v
-ifold alg (MkFix t) = alg v (Indexed.map (d v) (\ _ => ifold alg) t)
+ifold alg (MkFix t) = alg v (assert_total $ Indexed.map (d v) (\ _ => ifold alg) t)
diff --git a/libs/papers/Data/Description/Regular.idr b/libs/papers/Data/Description/Regular.idr
index 8e402fe5e..c4a0251f6 100644
--- a/libs/papers/Data/Description/Regular.idr
+++ b/libs/papers/Data/Description/Regular.idr
@@ -5,7 +5,7 @@
 
 module Data.Description.Regular
 
-%default covering
+%default total
 
 ||| Description of regular functors
 ||| @ p stores additional data for constant types
@@ -55,7 +55,7 @@ map d f = go d where
 ||| is total because we do not track positivity in function arguments
 public export
 data Fix : Desc p -> Type where
-  MkFix : Elem d (Fix d) -> Fix d
+  MkFix : assert_total (Elem d (Fix d)) -> Fix d
 
 namespace Example
 
@@ -94,7 +94,7 @@ infixr 0 ~>
 export
 record (~>) {p : Type -> Type} (d : Desc p) (b : Fix d -> Type) where
   constructor MkMemo
-  getMemo : Memo d (\ x => Inf (d ~> x)) (b . MkFix)
+  getMemo : assert_total (Memo d (\ x => Inf (d ~> x)) (b . MkFix))
 
 export
 trie : {d : Desc p} -> {0 b : Fix d -> Type} -> ((x : Fix d) -> b x) -> d ~> b
@@ -106,7 +106,7 @@ trie f = MkMemo (go d (\ t => f (MkFix t))) where
        Memo e (\ x => Inf (d ~> x)) b'
   go Zero f = ()
   go One f = f ()
-  go Id f = trie f
+  go Id f = assert_total trie f
   go (Const s prop) f = f
   go (d1 * d2) f = go d1 $ \ v1 => go d2 $ \ v2 => f (v1, v2)
   go (d1 + d2) f = (go d1 (\ v => f (Left v)), go d2 (\ v => f (Right v)))
diff --git a/libs/papers/Data/Enumerate.idr b/libs/papers/Data/Enumerate.idr
index 6f3261f71..251fb59f3 100644
--- a/libs/papers/Data/Enumerate.idr
+++ b/libs/papers/Data/Enumerate.idr
@@ -103,7 +103,7 @@ stream (MkEnumerator enum) = iterate enum []
 -- Defining generic enumerators for regular types
 ------------------------------------------------------------------------------
 
-covering export
+export
 regular : (d : Desc List) -> Enumerator (Fix d) (Fix d)
 regular d = MkFix <$> go d where
 
@@ -123,11 +123,9 @@ namespace Example
   lists : (xs : List a) -> Nat -> List (Fix (ListD xs))
   lists xs = sized (regular (ListD xs))
 
-  covering
   encode : {0 xs : List a} -> List a -> Fix (ListD xs)
   encode = foldr (\x, xs => MkFix (Right (x, xs))) (MkFix (Left ()))
 
-  covering
   decode : {xs : List a} -> Fix (ListD xs) -> List a
   decode = fold (either (const []) (uncurry (::)))
 
diff --git a/libs/papers/Data/Enumerate/Indexed.idr b/libs/papers/Data/Enumerate/Indexed.idr
index afbc04ec2..c7cad4b0f 100644
--- a/libs/papers/Data/Enumerate/Indexed.idr
+++ b/libs/papers/Data/Enumerate/Indexed.idr
@@ -86,7 +86,7 @@ isized f (S n) v = runIEnumerator (f v) (isized f n)
 -- Defining  generic enumerators for indexed datatypes
 ------------------------------------------------------------------------------
 
-covering export
+export
 indexed : (d : i -> IDesc List i) -> (v : i) -> IEnumerator (Fix d) (Fix d v)
 indexed d v = MkFix <$> go (d v) where
 
@@ -98,11 +98,11 @@ indexed d v = MkFix <$> go (d v) where
   go (d1 + d2) = Left <$> go d1 <|> Right <$> go d2
   go (Sig s vs f) = sig (const vs) (\ x => go (f x))
 
-export covering
+export
 0 Memorator : (d : Desc p) -> (Fix d -> Type) -> Type -> Type
 Memorator d a b = (d ~> (List . a)) -> List b
 
-export covering
+export
 memorate : {d : Desc p} ->
            {0 b : Fix d -> Type} ->
            ((x : Fix d) -> Memorator d b (b x)) ->